Constructal entransy dissipation rate minimization the problem of constracting “disc-point” cooling channels

Abstract

Based on configucation theory, the construction of a “disc-point” heat transfer with cooling channels can be optimized by taking minimum entransy dissipation rate. Thus an optimal construction of the disc-shaped assembly with cooling channels is obtained. The results show that there exists an optimal aspect ratio of the elemental sector which leads to the minimum dimensionless equivalent thermal resistance of the elemental sector at the fixed pumping power; there also exists an optimal width ratio of the elemental and first-order cooling channel to the optimal dimensionless radius of the elemental sector, which leads to the minimum dimensionless equivalent thermal resistance of the first-order branched-pattern disc at the fixed total pumping power. Moreover, the optimal width ratio of the elemental and first-order cooling channels is only relative to the number of elemental tributaries. When the radius of the central disc tends to zero, the branch-pattern disc is simplified into a radial-pattern disc, and the radius of the first-order branch-pattern disc becomes the critical radius at this point. When the radius of the branch-pattern disc is higher than the critical radius, the branch-pattern design should be adopted, otherwise the radial-pattern design should be adopted. There exists an optimal number of elemental tributaries which lead to the minimum dimensionless equivalent thermal resistance of the first-order branch-pattern disc, which is obviously different from the results of the “disc-point” heat conduction constructional optimization with high-conductivity channels. The optimal constructions of the first-order branch-pattern disc based on the minimizations of entransy dissipation rate and maximum temperature difference are different. The dimensionless equivalent thermal resistance of the disc with cooling channels based on the minimization of entransy dissipation rate is greatly reduced as compared with that based on the minimization of maximum temperature difference, and its global heat transfer performance is obviously improved simultaneously. Therefore, the combination of the entransy dissipation extremum principle and the heat convection constructional optimization further illustrates the advantages of minimization of entransy dissipation rate for heat transfer optimizations.